Ben Bradshaw said the warning, issued by scientists on Thursday, represented the world's biggest environmental challenge after global warming.
But he ruled out a complete ban on cod fishing, saying a "zero catch" would see "the end of all fishing in the UK".
UK fishermen's representatives have criticised the report as "grandiose".
The international study, published in the American journal, Science, said supplies of fish such as cod were under threat from over-fishing and habitat destruction.
The government had already clamped down on illegal fishing and set fishing quotas "in line with the health of stocks", Mr Bradshaw said.
"If there were to be a zero catch for cod, we would have to close almost all of the UK fishing industry because there's almost no part of our fishing industry that doesn't catch some cod as by-catch."
Measures taken in recent years had seen a 60% decrease in cod mortality rates, he said, which hopefully would continue.
Dr Nicola Beaumont from Plymouth Marine Laboratory was one of the scientists who helped draw up the report.
Source: BBC